Find out projection matrix for oblique projection, Computer Graphics

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Find Out Projection Matrix for Oblique Projection

To find out projection matrix for oblique projection, we want to find out the direction vector d. Because vector PP' and vector d both contain the same direction. Hence, PP'=d 

 So, x'- 0=d1= f.cosθ

       y'- 0=d2= f.sinθ

       z'-1=d3

 Since z'=0 on the xy-plane, d3 = -1, 

Because, Oblique projection is a particular case of parallel projection, hence, we can transform the common transformation of parallel projection for Oblique projection as given:

792_Find Out Projection Matrix for Oblique Projection.png

Here, f=foreshortening factor, that is the projected length of the z-axis unit vector. When β is the angle among the Oblique projectors and the plane of projection so,

1/f=tan (β) , that is f= cot(β)

θ=angle among the projected line along with the positive x-axis.


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